Harry Partch's 43-tone scale: Difference between revisions

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[[File:Harry Partch Institute-3.jpg|thumb|right|250px|The [[Quadrangularis Reversum]], one of Partch's instruments featuring the 43-tone scale]]

The '''43-tone scale''' is a [[just intonation]] scale with 43 pitches in each [[octave]]. It is based on an eleven-limit tonality diamond, similar to the seven-limit diamond previously devised by [[Max Friedrich Meyer]]<ref>[http://www.chrysalis-foundation.org/Meyer-s_Diamond.htm "Musical Mathematics: Meyer's Diamond"], ''Chrysalis-Foundation.org''.</ref> and refined by [[Harry Partch]].<ref>Kassel, R. (2001, January 20). Partch, Harry. [https://www.oxfordmusiconline.com/grovemusic/ ''Grove Music Online''].</ref>

The '''43-tone scale''' is a [[just intonation]] scale with 43 pitches in each [[octave]]. It is based on an eleven-limit [[tonality diamond]], similar to the seven-limit diamond previously devised by [[Max Friedrich Meyer]]<ref>[http://www.chrysalis-foundation.org/Meyer-s_Diamond.htm "Musical Mathematics: Meyer's Diamond"], ''Chrysalis-Foundation.org''.</ref> and refined by [[Harry Partch]].<ref>Kassel, R. (2001, January 20). Partch, Harry. [https://www.oxfordmusiconline.com/grovemusic/ ''Grove Music Online''].</ref>

See [[Partch 43]] for the scale as a scala file.

==Ratios of the 11 Limit==

[[File:11-odd-limit_Tonality_Diamond.png|thumb|Circle Digram]]

Here are all the ratios within the [[octave]] with odd factors up to and including 11, known as the 11-limit [[tonality diamond]]. Note that the [[Inversion (interval)|inversion]] of every interval is also present, so the set is symmetric about the octave.

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==Filling in the gaps==

[[File:Partch%27s_43_Tone_Scale.png|thumb|Circle diagram. (complete)]]

There are two reasons why the 11-limit ratios by themselves would not make a good scale. First, the scale only contains a complete set of chords ([[otonalities]] and [[utonalities]]) based on one [[tonic (music)|tonic]] pitch. Second, it contains large gaps, between the tonic and the two pitches to either side, as well as several other places. Both problems can be solved by filling in the gaps with "multiple-number ratios", or intervals obtained from the product or quotient of other intervals within the 11 limit.

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| 41 || 2/1 || 1200.00 || 1200.00 || 0.00

|}

== Comparison with 72edo ==

Since [[72edo]] is [[distinctly consistent]] in the 11-limit and is a [[pepper ambiguity]] record in the 11-limit unsurpassed until 270, 72edo fits very well the Harry Partch's 43-tone scale.

The mode is: 1 2 2 2 2 1 1 1 2 2 2 1 2 2 2 1 2 2 1 2 2 2 2 2 1 2 2 1 2 2 2 1 2 2 2 1 1 1 2 2 2 2 1

== Music ==

;[[Chris Ranier]]

* [https://chrisrainier.bandcamp.com/album/chris-rainier-sings-the-music-of-harry-partch ''Chris Ranier sings the music of Harry Partch](2024)

;[[The Rasa]]

* [https://www.youtube.com/watch?v=QwoOxiZRXFA ''Harry Partch's Rose Petal Jam''] (2020)

==References==

@@ Line 1: / Line 1: @@
 [[File:Harry Partch Institute-3.jpg|thumb|right|250px|The [[Quadrangularis Reversum]], one of Partch's instruments featuring the 43-tone scale]]
-The '''43-tone scale''' is a [[just intonation]] scale with 43 pitches in each [[octave]]. It is based on an eleven-limit tonality diamond, similar to the seven-limit diamond previously devised by [[Max Friedrich Meyer]]<ref>[http://www.chrysalis-foundation.org/Meyer-s_Diamond.htm "Musical Mathematics: Meyer's Diamond"], ''Chrysalis-Foundation.org''.</ref> and refined by [[Harry Partch]].<ref>Kassel, R. (2001, January 20). Partch, Harry. [https://www.oxfordmusiconline.com/grovemusic/ ''Grove Music Online''].</ref>
+The '''43-tone scale''' is a [[just intonation]] scale with 43 pitches in each [[octave]]. It is based on an eleven-limit [[tonality diamond]], similar to the seven-limit diamond previously devised by [[Max Friedrich Meyer]]<ref>[http://www.chrysalis-foundation.org/Meyer-s_Diamond.htm "Musical Mathematics: Meyer's Diamond"], ''Chrysalis-Foundation.org''.</ref> and refined by [[Harry Partch]].<ref>Kassel, R. (2001, January 20). Partch, Harry. [https://www.oxfordmusiconline.com/grovemusic/ ''Grove Music Online''].</ref>
 See [[Partch 43]] for the scale as a scala file.
 ==Ratios of the 11 Limit==
+[[File:11-odd-limit_Tonality_Diamond.png|thumb|Circle Digram]]
 Here are all the ratios within the [[octave]] with odd factors up to and including 11, known as the 11-limit [[tonality diamond]]. Note that the [[Inversion (interval)|inversion]] of every interval is also present, so the set is symmetric about the octave.
@@ Line 32: / Line 33: @@
 ==Filling in the gaps==
+[[File:Partch%27s_43_Tone_Scale.png|thumb|Circle diagram. (complete)]]
 There are two reasons why the 11-limit ratios by themselves would not make a good scale. First, the scale only contains a complete set of chords ([[otonalities]] and [[utonalities]]) based on one [[tonic (music)|tonic]] pitch. Second, it contains large gaps, between the tonic and the two pitches to either side, as well as several other places. Both problems can be solved by filling in the gaps with "multiple-number ratios", or intervals obtained from the product or quotient of other intervals within the 11 limit.
@@ Line 182: / Line 184: @@
 | 41 || 2/1 || 1200.00 || 1200.00 || 0.00
 |}
+== Comparison with 72edo ==
+Since [[72edo]] is [[distinctly consistent]] in the 11-limit and is a [[pepper ambiguity]] record in the 11-limit unsurpassed until 270, 72edo fits very well the Harry Partch's 43-tone scale.
+The mode is: 1 2 2 2 2 1 1 1 2 2 2 1 2 2 2 1 2 2 1 2 2 2 2 2 1 2 2 1 2 2 2 1 2 2 2 1 1 1 2 2 2 2 1
+== Music ==
+;[[Chris Ranier]]
+* [https://chrisrainier.bandcamp.com/album/chris-rainier-sings-the-music-of-harry-partch ''Chris Ranier sings the music of Harry Partch](2024)
+;[[The Rasa]]
+* [https://www.youtube.com/watch?v=QwoOxiZRXFA ''Harry Partch's Rose Petal Jam''] (2020)
 ==References==